Fine and nontangential convergence on an NTA domain
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- by J. C. Taylor PDF
- Proc. Amer. Math. Soc. 91 (1984), 237-244 Request permission
Abstract:
The recent article by Jerison and Kenig on "Boundary behaviour of harmonic functions in nontangentially accessible domains" did not consider the relation between fine limits and nontangential limits. The results in this direction obtained by Hunt & Wheeden [5] for Lipschitz domains are extended here to NTA domains.References
- M. Brelot and J. L. Doob, Limites angulaires et limites fines, Ann. Inst. Fourier (Grenoble) 13 (1963), no. fasc. 2, 395–415 (French). MR 196107
- J. L. Doob, Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. France 85 (1957), 431–458. MR 109961
- Kohur Gowrisankaran, Extreme harmonic functions and boundary value problems. II, Math. Z. 94 (1966), 256–270. MR 201660, DOI 10.1007/BF01111455
- L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1969. MR 0261018
- Richard A. Hunt and Richard L. Wheeden, Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc. 147 (1970), 507–527. MR 274787, DOI 10.1090/S0002-9947-1970-0274787-0
- Peter W. Jones, A geometric localization theorem, Adv. in Math. 46 (1982), no. 1, 71–79. MR 676987, DOI 10.1016/0001-8708(82)90054-8
- Peter W. Jones, A geometric localization theorem, Adv. in Math. 46 (1982), no. 1, 71–79. MR 676987, DOI 10.1016/0001-8708(82)90054-8
- Adam Korányi and J. C. Taylor, Fine convergence and admissible convergence for symmetric spaces of rank one, Trans. Amer. Math. Soc. 263 (1981), no. 1, 169–181. MR 590418, DOI 10.1090/S0002-9947-1981-0590418-1
- Linda Naïm, Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Ann. Inst. Fourier (Grenoble) 7 (1957), 183–281 (French). MR 100174
- J. C. Taylor, An elementary proof of the theorem of Fatou-Naïm-Doob, 1980 Seminar on Harmonic Analysis (Montreal, Que., 1980) CMS Conf. Proc., vol. 1, Amer. Math. Soc., Providence, R.I., 1981, pp. 153–163. MR 670103
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 237-244
- MSC: Primary 31B25; Secondary 31A20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740178-4
- MathSciNet review: 740178